So, for future designs of upgrades, it could be a good idea to place a pull up.

I think only if you have external (pull down?) loads on PSEN ?

A PSEN normally not connected, will not be pulled low.
I measured -27uA on a gnded pin, and -225uA on ~1.85V, so it is a QuasiIO pin, during RST active. After reset exit, it has a strong pullup (-18mA)

Boot mode is entered if PSEN is seen to be low on RST de-assert.

Koen De Ganck said:

I updated about 20 boards with a pull-up of 560K on pin 'PSEN'.
All but 1 board started up in a good way (10-20 tries), although most of them failed many times without pull-up.
The single board that had 1 failure out of 20, worked well with a pull-up of 330K.

While is it nice to know the boundary condition, I would fit well under 330K to allow for temperature and device margins.

Koen De Ganck said:

PSEN : is loaded with 1 port, the traces are within 2 x 3cm (4 endpoints ) on a multilayer.

What exactly is this load ?

Koen De Ganck said:

I also remove the LM810 reset chip as this is not needed anymore as the board works on 3V3.

I thought something else was driven by RST ?
I know a SW reset will drive out on RST pin, but I'm not sure if Power-Up does ?